How can I use the Point feature to leave a trail though all of the points it's passed through?

Question

I have a code in which I use the Manipulate feature to cause a point to oscillate along a line which is being rotated. What I've been trying to figure out is how to make the point leave a trail though all of the points that it travels through. I've tried to use a LineListPlot using 0,0 as the starting point and 0,Cos[Pi*6*x] as the end thinking that it would continually update the second point, but that didn't work. Here's the code

Manipulate[
 Graphics[
  Rotate[{{Red, Rectangle[{-(1/128), -2}, {1/128, 2}]}, {Blue, PointSize[0.02], Point[{0, Cos[\[Pi]*6*x]}]}},
   360 Degree*(6*x)],
  PlotRange -> {{-2.5, 2.5}, {-2, 2}},
  Axes -> True],
 {x, 0, 1}]

Answer 1

An easy way is to create a table of points that you have visited. Mathematica should be fast enough to do this on each update. In this setting, I recommend that you rather use a RotationMatrix m because it can be applied to each point instead of rotating the whole graphics:

Manipulate[
 DynamicModule[{m, trail},
  m[x_] := RotationMatrix[6 x];
  trail = Table[m[xx].{0, Cos[\[Pi]*6*xx]}, {xx, 0, x, 0.01}];
  Graphics[{
    PointSize[0.01], Green, Line[trail], Point[trail],
    Red, Line[{m[x].{0, -2}, m[x].{0, 2}}], Blue, PointSize[0.02], 
    Point[m[x].{0, Cos[\[Pi]*6*x]}]
    }, PlotRange -> {{-2.5, 2.5}, {-2, 2}}, Axes -> True]
  ], {x, 0, Pi}]